English

Verma modules over p-adic Arens-Michael envelopes of reductive Lie algebras

Representation Theory 2013-06-26 v2 Number Theory

Abstract

Let K be a locally compact nonarchimedean field, g a split reductive Lie algebra over K and U(g) its universal enveloping algebra. We study the category C_g of coadmissible modules over the nonarchimedean Arens-Michael envelope of U(g). Let p be a parabolic subalgebra of g. The main result identifies a certain explicitly given highest weight category inside C_g with the classical parabolic BGG category of g relative to p. This paper is in final form, replaces and expands the former preprint 'BGG reciprocity for p-adic Arens-Michael envelopes of semisimple Lie algebras' and appears in Journal of Algebra.

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Cite

@article{arxiv.1008.3897,
  title  = {Verma modules over p-adic Arens-Michael envelopes of reductive Lie algebras},
  author = {Tobias Schmidt},
  journal= {arXiv preprint arXiv:1008.3897},
  year   = {2013}
}

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21 pages